Resolution; Response Resolution - Agilent Technologies 8753ET User Manual

Making Time Domain Measurements

Resolution

Resolution
Two different resolution terms are used in the time domain:

• response resolution

• range resolution
Response Resolution
Time domain response resolution is defined as the ability to resolve two closely-spaced
responses, or a measure of how close two responses can be to each other and still be
distinguished from each other. For responses of equal amplitude, the response resolution is
equal to the 50% (−6 dB) impulse width. It is inversely proportional to the measurement
frequency span, and is also a function of the window used in the transform. The
approximate formulas for calculating the 50% impulse width are given in
example, using the formula for the bandpass mode with a normal windowing function for a
50 MHz to 13.05 GHz measurement (13.0 GHz span):
50 percent calculated impulse width
=
0.151 nanoseconds
(
Electrical length
=
4.53 centimeters
With this measurement, two equal responses can be distinguished when they are
separated by at least 4.53 centimeters. In a measurement with a 20 GHz span, two equal
responses can be distinguished when they are separated by at least 2.94 cm. Using the low
pass mode (the low pass frequencies are slightly different) with a minimum windowing
function, you can distinguish two equal responses that are about 1.38 centimeters or more
apart.
For reflection measurements, which measure the two-way time to the response, divide the
response resolution by 2. Using this example, you can distinguish two faults of equal
magnitude provided they are 0.69 centimeters (electrical length) or more apart.
NOTE Remember, to determine the physical length, the relative velocity factor of the
transmission medium under test must be entered into the electrical length
equation.
For example, a cable with a teflon dielectric (0.7 relative velocity factor), measured under
the conditions stated above, has a fault location measurement response resolution of 0.45
centimeters. This is the maximum fault location response resolution. Factors such as
reduced frequency span, greater frequency domain data windowing, and a large
3-32

)
×
=
in air
0.151

0.98
×
= -------------------------- - 2
( )
13.0 GHz


× 9
×
9 – 
30 10
10 s


Table 3-3. For

c m

--- -

s